1) I have three 2 pence pieces and two 10 pence pieces in my pocket. I pick two coins out of my pocket at random. Find the probability that the first coin was a 2 pence piece given that the coins were both the same.

2) The event T is that the sum of the coins' values is 20 pence and the event S is that the coins are the same.

a)Find the probability of T given that the coins are the same.
b)State with a reason, whether or not events S and T are independent.

Thanks in advance :)

Nov 20th 2006, 03:05 PM

Quick

when you say the coins are the same, do you mean that they are the same size and that they have equal chances of being drawn?

Nov 20th 2006, 05:09 PM

ThePerfectHacker

Quote:

Originally Posted by Quick

when you say the coins are the same, do you mean that they are the same size and that they have equal chances of being drawn?

Equla chances of being drawn.

Nov 20th 2006, 09:58 PM

CaptainBlack

Quote:

Originally Posted by Confuzzled?

1) I have three 2 pence pieces and two 10 pence pieces in my pocket. I pick two coins out of my pocket at random. Find the probability that the first coin was a 2 pence piece given that the coins were both the same.

The probability of drawing two 2p peices is (3/5)(2/4)=3/10.
The probability of drawing two 10p pieces is (2/5)(1/4)=1/10.

So in 100000 repeats of the experiment we would get close to 30000
cases where 2x2p are drawn and 10000 where 2x10p are drawn, and of
these 40000 cases where the two coints are the same in 30000 of them
the first coin drawn was a 2p, so the required probability is: